Question

sin theta - cos theta +1/cos theta + sin theta -1 = 1 /sec theta - tan theta​

Answer 1

Step-by-step explanation:

(sin θ - cos θ +1)/(cos θ + sin θ -1) = 1 /(sec θ - tan θ)

LHS = 1 /{(1 / cos θ) - (sin θ / cos θ)};

= 1 /{(1 - sin θ) / cos θ};

= cos θ/ (1 - sin θ);

(sin θ - cos θ +1)/(cos θ + sin θ -1) = cos θ/ (1 - sin θ);

(sin θ - cos θ +1)×(1 - sin θ) = cos θ×(cos θ + sin θ -1);

sin θ -sin^2 θ -cos θ +cos θsinθ +1 -sin θ = cos^2 θ + cos θsin θ -cos θ.

-sin^2 θ -cos θ +cos θsinθ +1 = cos^2 θ + cos θsin θ -cos θ.

-sin^2 θ +1 = cos^2 θ

1 = cos^2 θ + sin^2 θ;

1 = 1; (since, cos^2 θ + sin^2 θ = 1)

Thus, LHS = RHS.

That's all.